On the consistency of non-minimally coupled f(R) gravity

TL;DR

This paper investigates the theoretical consistency of non-minimally coupled f(R) gravity theories, deriving conditions to avoid instabilities and ghosts, and constraining the forms of permissible coupling functions.

Contribution

It provides a systematic analysis of stability conditions for non-minimal couplings in f(R) gravity using scalar field models, restricting viable coupling functions.

Findings

Power-law couplings are viable only for sublinear positive powers.

Certain coupling functions are ruled out due to instabilities.

Derived conditions prevent ghosts and superluminal propagation.

Abstract

Theories with a non-minimal coupling between the space-time curvature and matter fields introduce an extra force due to the non-conservation of the matter energy momentum. In the present work the theoretical consistency of such couplings is studied using a scalar field Lagrangian to model the matter content. The conditions that the coupling does not introduce ghosts, classical instabilities or superluminal propagation of perturbations are derived. These consistency conditions are then employed to rule out or severely restrict the forms of the non-minimal coupling functions considered in the previous literature. For example, a power-law coupling is viable only for sublinear positive power of the curvature scalar.